One solution for simultaneously dispensing a plurality of measured quantities of a liquid into individual treatment vessels consists in providing as many valves as there are vessels, the valves being connected firstly to a common source of said liquid, and secondly to filler orifices opening out respectively into said vessels. The time each valve is open serves to control the quantity of liquid dispensed. That solution rapidly becomes very expensive to implement when the treatment vessels are numerous and a plurality of successive treatment or rinsing liquids need to be delivered to the vessels, since the number of valves needs to be multiplied accordingly. Also, there can be a problem of bulk due to the number of valves.